I n bioassay, where different levels of the stimulus may represent different doses of a drug, the binary response is the death or survival of an individual receiving a specified dose. I n such applications, it is common to model the probability of a positive response P a t tlie stimulus level z by P =F(z'j3), where F is a cumulative distribution function and fi is a vector of unknown parameters which cKaracterize the response function. The two most popuiar models used for modelling binary response bioassay involve the probit model [BLISS (1935), FI"EY (1978)], and t h e logistic model [BERKSON (1944), BROWN (1982)l. However, these models have some limitations. The use of the probit model involves the inverse of the standard normal distribution function, making i t rather intractable. The logistic model has a simple form and a closed expression for the inverse distribution function, however, neither t h e logistic nor the probit can provide a good fit to response functions which are not symmetric or are symmetric but have D steeper or gentler incline in the central probability region. In this paper we introduce a more realistic model for the analysis of quanta1 response bioaesay. The proposed model, which we refer t o i t as t h e generalized logistic model, is a family of response curves indexed by shape parameters mi and %. This family is rich enough to include the probit and logistic models as well aa many others as special cases or limiting distributions.
In particular, we consider tlie generalized logistic three parameter model where we assume that m,=m, v1 is a positive real number, and % = I . We apply this model t o various sets of data, comparing the fit results to those obtained previously by other dose-response curves such as the logistic and probit, and showing that the fit can be improved by using the generalized logistic.